I want to use a arduino mini to take 4 channels from my RC receiver (pwm) and control a camera zoom, focus, etc. The camera has the leads that control the camera when grounded. so, if I ground one lead, it zooms in, another lead it zooms out, another lead focus near, another lead focus far etc. So, would I need to have relays for each lead or can the arduino short the leads to ground by itself? Anyone have a similar set of code to get me started?

You need to know the voltage on those leads, and how much current they flow when they're shorted to ground. If it's less than 5V and about 20mA then the Arduino can sink it directly, otherwise you'd need to go through a transistor.

I only provide help via the forum - please do not contact me for private consultancy.